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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

5 votes
0 answers
139 views

Complementary Bell numbers $B^{\pm}(24n+14)$

The complementary Bell numbers $B^{\pm}(n)$ are defined by the alternating sum of the Stirling numbers of the second kind, $S(n,k)$: $$B^{\pm}(n)=\sum_{k=0}^n(-1)^kS(n,k),$$ and they count the differe …
Valerio_xula's user avatar
3 votes

Asymptotic expansion for the Bell numbers

The answer to this question is yes, the series is absolutely convergent for all large enough values of $n$, as I recently found out. It is discussed earlier on in de Bruijn's book "Asymptotic methods …
Valerio_xula's user avatar